def plot_bumps_on_data(X, bumps, palette='Set1'):
plot_data_embedded(X, palette='w')
colors = sns.color_palette(palette, n_colors=len(bumps))
colors = [mpl_colors.to_hex(c) for c in colors]
np.random.shuffle(colors)
for i, (b, c) in enumerate(zip(bumps, colors)):
alpha = np.maximum(b, 0) / b.max()
plot_data_embedded(X, palette=c, alpha=alpha)
def process_curves():
with open('bunny_processed.pickle', mode='r+b') as f:
bunny_dict = pickle.load(f)
circle_clustered_dict = pickle.load(f)
plt.figure(figsize=(10, 6), tight_layout=True)
gs = gridspec.GridSpec(3, 6)
bunny_idx = [0, 40, 80, 174, 524, 699]
# bunny_idx = np.linspace(0, len(bunny_dict) - 1, num=5, endpoint=True,
# dtype=np.int)
for i, idx in enumerate(bunny_idx):
print(idx)
curve = bunny_dict[idx]
Y = sdp_km_burer_monteiro(curve, 20, rank=len(curve),
tol=1e-6, maxiter=5000, verbose=True)
Q = Y.dot(Y.T)
labels = np.arange(len(curve))
ax = plt.subplot(gs[0, i])
plot_data_embedded(curve, s=2, ax=ax)
ax = plt.subplot(gs[1, i])
plot_matrix(Q, labels=labels, labels_palette='hls', ax=ax)
ax = plt.subplot(gs[2, i])
plot_bumps_1d(Y, subsampling=10, labels=labels, labels_palette='hls',
ax=ax)
plt.savefig(dir_name + 'bunny_deformation.pdf', dpi=300)
plt.show()
plt.figure(figsize=(10, 6), tight_layout=True)
gs = gridspec.GridSpec(3, 6)
circle_idx = [1, 3, 5, 7, 10, 199]
# circle_idx = np.linspace(1, len(circle_clustered_dict), num=5,
# endpoint=True, dtype=np.int)
for i, idx in enumerate(circle_idx):
print(idx)
curve = circle_clustered_dict[idx]
Y = sdp_km_burer_monteiro(curve, 4, rank=len(curve),
tol=1e-6, maxiter=5000, verbose=True)
Q = Y.dot(Y.T)
labels = np.arange(len(curve))
ax = plt.subplot(gs[0, i])
plot_data_embedded(curve, s=2, ax=ax)
ax = plt.subplot(gs[1, i])
plot_matrix(Q, labels=labels, labels_palette='hls', ax=ax)
ax = plt.subplot(gs[2, i])
plot_bumps_1d(Y, subsampling=15, labels=labels, labels_palette='hls',
ax=ax)
plt.savefig(dir_name + 'circle_deformation.pdf', dpi=300)
plt.show()
def plot_bumps_on_data(X, bumps, palette='Set1', ax=None):
if ax is None:
ax = plt.gca()
plot_data_embedded(X, palette='w', edgecolors='k', ax=ax)
colors = sns.color_palette(palette, n_colors=len(bumps))
colors = [mpl_colors.to_hex(c) for c in colors]
np.random.shuffle(colors)
for i, (b, c) in enumerate(zip(bumps, colors)):
alpha = np.maximum(b, 0) / b.max()
plot_data_embedded(X, palette=c, alpha=alpha, edgecolors='none', ax=ax)
def plot_bumps_on_data(X, bumps, palette='Set1', ax=None):
if ax is None:
ax = plt.gca()
# Plot the sphere
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
ax.plot_surface(0.99 * np.outer(np.cos(u), np.sin(v)),
0.99 * np.outer(np.sin(u), np.sin(v)),
0.99 * np.outer(np.ones(np.size(u)), np.cos(v)),
color='w',
edgecolors='#AAAAAA',
alpha=1)
plot_data_embedded(X, palette='w', edgecolors='k', ax=ax)
colors = sns.color_palette(palette, n_colors=len(bumps))
colors = [mpl_colors.to_hex(c) for c in colors]
for i, (b, c) in enumerate(zip(bumps, colors)):
alpha = np.maximum(b, 0) / b.max()
plot_data_embedded(X, palette=c, alpha=alpha, edgecolors='none', ax=ax)
def test_grid(n_clusters=16, use_copositive=False):
X = np.mgrid[0:16, 0:16]
X = X.reshape((len(X), -1)).T
labels = np.arange(len(X))
# X_norm = X - np.mean(X, axis=0)
# cov = X_norm.T.dot(X_norm)
# X_norm /= np.trace(cov.dot(cov)) ** 0.25
#
# alpha = 0.001
# plt.matshow(np.maximum(X_norm.dot(X_norm.T) - alpha, 0), cmap='gray_r')
#
# from scipy.spatial.distance import pdist, squareform
# plt.matshow(squareform(pdist(X)), cmap='gray_r')
#
# return
rank = len(X)
print(rank)
if use_copositive:
beta = n_clusters / len(X)
Y = copositive_burer_monteiro(X,
alpha=0.003,
beta=beta,
rank=rank,
tol=1e-5,
constraint_tol=1e-5,
verbose=True)
name = 'grid_copositive_bm'
else:
Y = sdp_km_burer_monteiro(X,
n_clusters,
rank=rank,
tol=1e-6,
verbose=True)
name = 'grid_sdpkm_bm'
Q = Y.dot(Y.T)
idx = np.argsort(np.argmax(Y, axis=0))
Y = Y[:, idx]
sns.set_style('white')
plt.figure(figsize=(12, 4.7), tight_layout=True)
gs = gridspec.GridSpec(1, 3)
ax = plt.subplot(gs[0])
plot_data_embedded(X, palette='hls', ax=ax)
plt_title = ax.set_title('Input dataset', fontsize='xx-large')
# plt_title.set_position((0.5, 1.07))
ax = plt.subplot(gs[1])
plot_matrix(Q,
ax=ax,
labels=labels,
which_labels='both',
labels_palette='hls')
plt_title = ax.set_title(r'$\mathbf{Q}$', fontsize='xx-large')
plt_title.set_position((0.5, 1.07))
ax = plt.subplot(gs[2])
plot_matrix(Y,
ax=ax,
labels=labels,
which_labels='vertical',
labels_palette='hls')
plt_title = ax.set_title(r'$\mathbf{Y}^\top$', fontsize='xx-large')
plt_title.set_position((0.5, 1.07))
plt.savefig('{}{}.pdf'.format(dir_name, name))
pdf_file_name = '{}{}_plot_{}_on_data_{}{}'
for i in range(Y.shape[1]):
plt.figure()
plot_bumps_on_data(X, [Y[:, i]])
plt.savefig(pdf_file_name.format(dir_name, name, 'Y', i, '.png'),
dpi=300,
bbox_inches='tight')
plt.close()
pdf_file_name = '{}{}_plot_{}_on_data_{}'
plt.figure()
bumps_locs = np.random.random_integers(Y.shape[1], size=6)
plot_bumps_on_data(X, [Y[:, i] for i in bumps_locs], palette='Set1')
plt.savefig(pdf_file_name.format(dir_name, name, 'Y', 'multiple.png'),
dpi=300,
bbox_inches='tight')
Y_aligned = align_bumps(Y, Y.shape[1] // 2)
_, ax = plt.subplots(1, 1)
plot_matrix(Y_aligned, ax=ax)
plt_title = ax.set_title(r'Aligned $\mathbf{Y}^\top$', fontsize='xx-large')
plt_title.set_position((0.5, 1.07))
plt.savefig('{}{}_Y_aligned_2d.pdf'.format(dir_name, name))
_, ax = plt.subplots(1, 1)
ax.plot(Y_aligned)
ax.set_xticks([])
ax.set_yticks([])
ax.set_title(r'Receptive fields', fontsize='xx-large')
plt.savefig('{}{}Y_aligned_1d.pdf'.format(dir_name, name))
pos = np.arange(len(Y))
median = np.median(Y_aligned, axis=1)
mu = np.mean(Y_aligned, axis=1)
sigma = np.std(Y_aligned, axis=1)
_, ax = plt.subplots(1, 1)
plt_mean = ax.plot(pos, mu, color='#377eb8')
ax.fill_between(pos,
np.maximum(mu - 3 * sigma, 0),
mu + 3 * sigma,
alpha=0.3,
color='#377eb8')
plt_median = ax.plot(pos, median, '-.', color='#e41a1c')
ax.set_xticks([])
ax.set_yticks([])
plt_aux = ax.fill(np.NaN, np.NaN, '#377eb8', alpha=0.3, linewidth=0)
ax.legend([(plt_mean[0], plt_aux[0]), plt_median[0]],
[r'Mean $\pm$ 3 STD', 'Median'],
loc='upper left',
fontsize='xx-large')
ax.set_title(r'Receptive fields summary', fontsize='xx-large')
plt.savefig('{}{}Y_aligned_1d_summary.pdf'.format(dir_name, name))
def test_toy_embedding(X,
Y,
target_dim,
filename,
palette='hls',
elev_azim=None):
print('--------\n', filename)
embedding = spectral_embedding(Y,
target_dim=target_dim,
gramian=False,
discard_first=False)
D = dot_matrix(X)
Q = Y.dot(Y.T)
labels = np.arange(len(X))
sns.set_style('white')
plt.figure(figsize=(20, 5), tight_layout=True)
gs = gridspec.GridSpec(1, 5)
if X.shape[1] == 3:
ax = plt.subplot(gs[0], projection='3d')
else:
ax = plt.subplot(gs[0])
plot_data_embedded(X, ax=ax, palette=palette, elev_azim=elev_azim)
ax.set_title('Input dataset', fontsize='xx-large')
titles = [
r'Input Gramian $\mathbf{X}^\top \mathbf{X}$',
r'$\mathbf{Y}^\top \mathbf{Y}$'
]
for i, (M, t) in enumerate(zip([D, Q], titles)):
ax = plt.subplot(gs[i + 1])
plot_matrix(M,
ax=ax,
labels=labels,
which_labels='both',
labels_palette=palette,
colorbar_labelsize=15)
plt_title = ax.set_title(t, fontsize=25)
plt_title.set_position((0.5, 1.07))
ax = plt.subplot(gs[3])
plot_matrix(Y,
ax=ax,
labels=labels,
which_labels='vertical',
labels_palette=palette,
colorbar_labelsize=15)
title_y = r'$\mathbf{Y}^\top$ ($'
plt_title = ax.set_title(title_y, fontsize=25)
plt_title.set_position((0.5, 1.07))
if target_dim == 2:
ax = plt.subplot(gs[4])
if target_dim == 3:
ax = plt.subplot(gs[4], projection='3d')
plot_data_embedded(embedding, ax=ax, palette=palette)
ax.set_title('2D embedding', fontsize=25)
plt.savefig('{}{}.pdf'.format(dir_name, filename), dpi=300)
fig = plt.figure()
if target_dim == 2:
ax = fig.add_subplot(111)
if target_dim == 3:
ax = fig.add_subplot(111, projection='3d')
plot_data_embedded(embedding, ax=ax, palette=palette)
plt.savefig('{}{}_embedding.pdf'.format(dir_name, filename), dpi=300)
# pdf_file_name = '{}{}_plot_{}_on_data_{}{}'
# for i in range(Y.shape[1]):
# plt.figure()
# plot_bumps_on_data(embedding, [Y[:, i]])
# plt.savefig(pdf_file_name.format(dir_name, filename, 'Y', i, '.png'),
# dpi=300)
# plt.close()
pdf_file_name = '{}{}_plot_{}_on_data_{}'
plt.figure()
if target_dim == 2:
ax = fig.add_subplot(111)
if target_dim == 3:
ax = fig.add_subplot(111, projection='3d')
plot_bumps_on_data(embedding, [Y[:, i] for i in range(0, Y.shape[1], 10)],
ax=ax)
plt.savefig(pdf_file_name.format(dir_name, filename, 'Y', 'multiple.pdf'),
dpi=300)
pdf_file_name = '{}{}_plot_{}_1d{}'
_, ax = plt.subplots(1, 1)
plot_bumps_1d(Y, subsampling=10, labels=labels, ax=ax)
ax.set_yticks([])
ax.set_title(r'Rows of $\mathbf{Y}$', fontsize=25)
plt.savefig(pdf_file_name.format(dir_name, filename, 'Y', '.pdf'), dpi=300)
def test_one_circle(n_clusters=25, use_copositive=False):
np.random.seed(10)
X = sphere.generate_sphere_grid()
print(X.shape)
labels = np.arange(len(X))
rank = 4 * n_clusters
print(rank)
if use_copositive:
beta = n_clusters / len(X)
Y = copositive_burer_monteiro(X,
alpha=0.0048,
beta=beta,
rank=rank,
tol=1e-6,
constraint_tol=1e-6,
verbose=True)
name = 'sphere_copositive_bm'
else:
Y = sdp_km_burer_monteiro(X,
n_clusters,
rank=rank,
tol=1e-5,
verbose=True)
name = 'sphere_sdpkm_bm'
Q = Y.dot(Y.T)
idx = np.argsort(np.argmax(Y, axis=0))
Y = Y[:, idx]
Y_aligned = align_bumps(Y, Y.shape[1] // 2)
scipy.io.savemat(name + '.mat', {'X': X, 'Y': Y})
sns.set_style('white')
plt.figure(figsize=(12, 5), tight_layout=True)
gs = gridspec.GridSpec(1, 3)
ax = plt.subplot(gs[0], projection='3d')
plot_data_embedded(X, palette='hls', ax=ax)
ax.set_title('Input dataset', fontsize='xx-large')
ax = plt.subplot(gs[1])
plot_matrix(Q,
ax=ax,
labels=labels,
which_labels='both',
labels_palette='hls')
plt_title = ax.set_title(r'$\mathbf{Q}$', fontsize='xx-large')
plt_title.set_position((0.5, 1.07))
ax = plt.subplot(gs[2])
plot_matrix(Y,
ax=ax,
labels=labels,
which_labels='vertical',
labels_palette='hls')
plt_title = ax.set_title(r'$\mathbf{Y}^\top$', fontsize='xx-large')
plt_title.set_position((0.5, 1.07))
plt.savefig('{}{}.pdf'.format(dir_name, name), dpi=300)
def test_one_circle(X,
Y,
name,
bump_subsampling=20,
cos_freq=0.13,
cos_loc=None):
labels = np.arange(len(X))
Q = Y.dot(Y.T)
idx = np.argsort(np.argmax(Y, axis=0))
Y = Y[:, idx]
Y_aligned = align_bumps(Y, Y.shape[1] // 2)
sns.set_style('white')
plt.figure(figsize=(12, 5), tight_layout=True)
gs = gridspec.GridSpec(1, 3)
ax = plt.subplot(gs[0])
plot_data_embedded(X, palette='hls', ax=ax)
ax.set_title('Input dataset', fontsize=30)
ax = plt.subplot(gs[1])
plot_matrix(Q,
ax=ax,
labels=labels,
which_labels='both',
labels_palette='hls',
colorbar_labelsize=15)
plt_title = ax.set_title(r'$\mathbf{Y}^\top \mathbf{Y}$', fontsize=25)
plt_title.set_position((0.5, 1.07))
ax = plt.subplot(gs[2])
plot_matrix(Y,
ax=ax,
labels=labels,
which_labels='vertical',
labels_palette='hls',
colorbar_labelsize=15)
plt_title = ax.set_title(r'$\mathbf{Y}^\top$', fontsize=25)
plt_title.set_position((0.5, 1.07))
plt.savefig('{}{}.pdf'.format(dir_name, name), dpi=300)
# pdf_file_name = '{}{}_plot_{}_on_data_{}{}'
# for i in range(Y.shape[1]):
# plt.figure()
# plot_bumps_on_data(X, [Y[:, i]])
# plt.savefig(pdf_file_name.format(dir_name, name, 'Y', i, '.png'),
# dpi=300)
# plt.close()
pdf_file_name = '{}{}_plot_{}_on_data_{}'
plt.figure()
bumps_locs = np.linspace(0,
Y.shape[1],
num=6,
endpoint=False,
dtype=np.int)
plot_bumps_on_data(X, [Y[:, i] for i in bumps_locs], palette='Set1')
plt.savefig(pdf_file_name.format(dir_name, name, 'Y', 'multiple.png'),
dpi=300)
_, ax = plt.subplots(1, 1)
plot_matrix(Y_aligned, ax=ax)
plt_title = ax.set_title('Aligned receptive fields', fontsize=25)
plt_title.set_position((0.5, 1.07))
plt.savefig('{}{}_Y_aligned_2d.pdf'.format(dir_name, name), dpi=300)
_, ax = plt.subplots(1, 1)
plot_bumps_1d(Y, labels=labels, ax=ax, subsampling=bump_subsampling)
ax.set_title('Receptive fields', fontsize=25)
plt.savefig('{}{}Y_1d.pdf'.format(dir_name, name), dpi=300)
_, ax = plt.subplots(1, 1)
ax.plot(Y_aligned)
ax.set_xticks([])
ax.set_yticks([])
ax.set_title('Aligned receptive fields', fontsize=25)
plt.savefig('{}{}Y_aligned_1d.pdf'.format(dir_name, name), dpi=300)
pos = np.arange(len(Y))
# median = np.median(Y_aligned, axis=1)
mu = np.mean(Y_aligned, axis=1)
sigma = np.std(Y_aligned, axis=1)
def cosine(x):
peak = np.argmax(mu)
if cos_loc is None:
cloc = np.mean(np.where(mu == mu[peak])[0])
else:
cloc = cos_loc
cos_bump = mu[peak] * np.cos(cos_freq * (x - cloc))
cos_bump[mu == 0] = 0
cos_bump[cos_bump < 0] = 0
return cos_bump
_, ax = plt.subplots(1, 1)
plt_mean = ax.plot(pos, mu, color='#377eb8')
ax.fill_between(pos,
np.maximum(mu - 3 * sigma, 0),
mu + 3 * sigma,
alpha=0.3,
color='#377eb8')
plt_cosine = ax.plot(pos, cosine(pos), '-.', color='#e41a1c')
ax.set_xticks([])
ax.set_yticks([])
plt_aux = ax.fill(np.NaN, np.NaN, '#377eb8', alpha=0.3, linewidth=0)
ax.legend([(plt_mean[0], plt_aux[0]), plt_cosine[0]],
[r'Mean $\pm$ 3 STD', 'Truncated cosine'],
loc='center left',
fontsize=25)
ax.set_title(r'Receptive fields summary', fontsize=25)
plt.savefig('{}{}Y_aligned_1d_summary.pdf'.format(dir_name, name), dpi=300)